Not likely. A non-nuclear "dirty bomb" is unlikely to be very efficient in dispersing radioactivity. The particulates formed will fall out quickly, and are among the easier things to detect and clean up.

The only real value in such a device is the "scare factor" associated with the word "nuclear".

You don’t know anything of the sort. You may be thinking 2D when it is entirely possible that one of these things could go off atop a 30 story or higher building. How do you clean up windborne particulate then? I suggest you think a bit more about it.